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## Homework Statement

An extra electron is added to one atom of a tri-atomic molecule. The electron has equal probability to jump to either of the other two atoms.

(a) Find the eigen-energies for the system. Assume that the new electron energy ##\bar{E_{0}}## is close to the non-hopping case energy ##E_{0}##. Draw an energy level diagram.

(b) Find one normalized eigenstate for the system.

## Homework Equations

## The Attempt at a Solution

(a) The only information available to me are that the the electron has equal probability to jump to either of the other two atoms. and the system has three atoms. How can these two pieces of information be used to find the eigen-energies of the system? Am I missing something?